Let x represent the side length of the square end, and let d represent the dimension that is the sum of length and girth. Then the volume V is given by
V = x²(d -4x)
Volume will be maximized when the derivative of V is zero.
dV/dx = 0 = -12x² +2dx
0 = -2x(6x -d)
This has solutions
x = 0, x = d/6

a) The largest possible volume is
(d/6)²(d -4d/6) = 2(d/6)³
= 2(108 in/6)³ = 11,664 in³

b) The dimensions of the package with largest volume are
d/6 = 18 inches square by
d -4d/6 = d/3 = 36 inches long

8 0

2 years ago

Find the probability of atleast three successes in six trials of a binomial experiment in which the probability of success is 50

yan [13]

The binomial cumulative probability with p=0.5 for 3+ successes is as follows:

$P(3+)=\sum_{k=3}^6 {{6}\choose{k}}p^k(1-p)^{6-k}$

for p=0.5 (50% success rate) it becomes:

$P(3+)=\sum_{k=3}^6 {{6}\choose{k}}0.5^6=\frac{21}{32}=0.65625$

the probability is 0.65625, or about 66%

7 0

2 years ago

Solve the quadratic equation.<br> 4x2 - 9 = 0

fenix001 [56]

(2x +3)(2x-3)= 0

x= -3/2 x = 3/2

4 0

2 years ago

Read 2 more answers

What is 40,023,032 in expanded form

Tanya [424]

40,023,032 = (4 x 1000000000) + (0 x 100000000) + (0 x 10000000) + (0 x 1000000) + (2 x 100000) + (3 x 10000) + (0 x 1000) + (0 x 100) + (3 x 10) + (2 x 1)

4 0

2 years ago